Abstract
We outline four live scenarios for cosmic origins relative to "seeding": (i) natural self-generation, (ii) civilizational genesis by earlier minds, (iii) simulation, and (iv) we are early/first. Each admits observable footprints or decision-relevant bounds. We restore a detailed catalog of mathematical encoding options (carriers, codes, statistics, capacity/robustness, and selection formalism), propose concrete, falsifiable programs, and argue for τ-robust messages if "first" remains plausible.
Version Note
v1.1 additions: Decision tree; restored & expanded mathematical options; testable footprints table; τ-robust messaging; "we're first" governance; three pre-registrable program sketches.
1. Decision Tree
| Branch | Claim | Implications |
|---|---|---|
| Natural | Universes arise lawfully (inflation/bounce/black-hole budding) | Seeding is scientific extension; look for baseline relics (no engineered signals) |
| Civilizational genesis | Earlier minds seeded ours | Search for engineered encodings in early conditions/constants/topology |
| Simulation | Universe computed by an external agent | Proceed with standard tests; predictions & falsifiers still carry inside the sim |
| We are first/early | No prior seeders in our past light cone | Ethical stewardship; publish open protocols; multiple redundant messages |
2. Mathematical Options & Encoders
2.1 Carriers (where to put bits)
| Carrier | Handle | Noise Model | Pros / Cons |
|---|---|---|---|
| Topology | Compact spatial manifolds; matched circles | Cosmic variance; masking | Dimensionless & robust / low capacity, difficult inference |
| CMB spectrum & phases | Low-ℓ phase patterns; harmonic coefficients aℓm | Gaussian random field + systematics | Global visibility / strong multiple-testing penalties |
| Dimensionless constants | {α, me/mp, Q, Gℏ/c³, …} | Measurement error; drift | Simple & universal / very low capacity if stability is tight |
| Early-universe geometry | Features in inflationary potential; spectral running | Model dependence; degeneracies | Medium capacity / interpretability risk |
| Cosmic web morphology | Persistent homology; Euler characteristic χ | Nonlinear growth; bias | Topological redundancy / late-time contamination |
2.2 Codes & algebra (how to structure bits)
- Short, prime-length sequences: Barker-like, Legendre, m-sequences (GF(2) LFSR) for low autocorrelation sidelobes.
- Error-correcting codes: Hamming, BCH, Reed–Solomon, extended Golay (24,12,8) for compact payloads with parity/checksums.
- Group-theoretic placements: encode on irreps of SO(3) via selected aℓm with symmetry constraints.
- Balanced alphabets: ternary/biased codes to survive coarse graining; constant-weight codebooks for spectral carriers.
2.3 Statistics & tests (how to detect/reject)
- Compression tests (AIC/MDL proxies): does a candidate code reduce description length vs. null?
- Algorithmic proxies: LZ76/CTW complexity on carrier strings (pre-registered mapping from map → string).
- Autocorrelation & cross-correlation: max normalized deviation vs. Gaussian phase nulls.
- Multiple testing control: Bonferroni for small families; Benjamini–Hochberg (FDR) for broader scans.
- Bayesian comparison: Bayes factors with explicit code priors and noise models.
2.4 Capacity & robustness (how many bits survive)
Choose τenc,i (tolerated embedding amplitude) below detection thresholds that would break cosmology; model σi (noise) per carrier. Use repetition and interleaving to trade rate for reliability (Shannon).
2.5 Selection formalism (if universes reproduce)
Reproductive fitness F combines black-hole yield λBH and habitability H. Ridge tests: is our observed θ near ∇F ≈ 0 with a negative-definite Hessian?
2.6 Decoder pipelines (how a descendant would read)
- Carrier-specific preprocessing (masking, filtering, topology inference).
- Map to canonical strings/vectors (harmonic coefficients, ratio tuples, persistence barcodes).
- Apply pre-registered statistics; decode with ECC if parity bits present.
- Publish code, null ensembles, and decision thresholds.
2.7 Risk & ethics
Prefer diagnostic encodings that do not materially perturb structure formation. No payload should increase existential risk to downstream observers.
3. Observable Footprints & Tests
3.1 Engineered encodings (civilizational genesis)
| Target | What to look for | Test sketch | Notes |
|---|---|---|---|
| CMB low-ℓ morphology | Compressible, pre-specified short codes | Pre-register code family/statistic → apply to Planck/next CMB maps | Avoid p-hacking: single statistic, correction for look-elsewhere |
| Dimensionless constants | Encodable bits in measured values | Bound how many stable bits survive lab error & cosmic variance | Prefer ratios; publish negative result if infeasible |
| Topology | Preferred compactifications (circles/matches) | Hunt matched circles; constrain specific topologies | Conservative priors; replication across pipelines |
3.2 Natural baselines
- Bubble collisions/bounce relics: survey very-large-scale anomalies with pre-specified templates.
- No engineered codes: null strengthens the natural baseline.
3.3 "We're first" circumstantial bounds
- Galaxy-scale waste heat/technosignatures: aggregate upper limits → "no prior galaxy-scale engineers to redshift Z".
- Parameter selection: if reproductive selection acts (BH + life-friendly chemistry), are our constants near local yield ridges?
4. τ-Robust Message Design for Baby Universes
Messages should survive extreme coarse-graining and dissipation. Favor dimensionless, topological, and spectral encodings.
4.1 Principles
- Dimensionless invariants: use ratios (e.g., r ≡ α/αG) rather than units.
- Small alphabets: short prime-length sequences; error-correcting repetition.
- Orthogonality: place the same payload in multiple independent carriers (constants, topology, spectrum).
4.2 Example payload (toy)
Embed M as: (a) low-ℓ CMB phase pattern, (b) slight biases in a set of dimensionless ratios within error tolerance, (c) preferred compact topology signature.
5. If We're First: Safety & Governance
- Great Filter awareness: assume unknown failure modes; track leading indicators; use slow, staged deployments.
- Open pre-registration: time-stamped plans for searches and encodings to minimize bias and coordinate globally.
- Plural encoders: avoid single-point failure of culture/values; diversify payload custodians.
6. Programs & Pipelines (Pre-registrable)
6.1 CMB Code Search (low-ℓ)
- Specify a tiny code family before looking (e.g., prime-length Barker sequences up to N = 47).
- Define one statistic (normalized autocorrelation deviation), one mask, one null ensemble.
- Freeze the analysis; run on Planck maps and a held-out replication pipeline.
6.2 Bits-in-Constants Feasibility
- Choose a set of dimensionless constants and current 1σ uncertainties.
- Compute Shannon capacity under measurement noise + drift models.
- Report upper bound on encodable bits; negative results welcome.
6.3 Black-Hole Yield Sensitivity Map
- Vary a minimal parameter set (e.g., α, me/mp, Q, G).
- Simulate stellar IMF, lifetimes, BH formation, heavy-element yield.
- Publish contours; test whether our point lies on a ridge/plateau.
7. Falsifiers, Nulls, and Bounds
- Engineered encodings falsified: pre-reg code search returns consistent nulls across pipelines → disfavors civilizational-genesis messaging (not the whole branch).
- Messages-in-constants infeasible: capacity ≪ 1 bit under stability/noise → abandon that carrier; focus on topology/spectrum.
- Selection ridges absent: BH yield flat across neighborhood → weakens reproduction-based selection stories.
- Technosignature bounds: no galaxy-scale engineers to redshift Z → increases plausibility of "first/early."
References
- Standard cosmology texts on inflation, CMB, topology searches.
- Method papers on pre-registration, MDL, and multiple-testing control in cosmology.
- Information theory (Shannon capacity; error-correcting codes) and algorithmic complexity references.
- Prior discussions of cosmic selection (black-hole reproduction) and anthropic constraints.
- White, T. (2025). Unified Temporal—Energetic Geometry; τ-first messaging concepts.
Appendix A — CMB Code Search (Pre-Reg Sketch)
- Code family: Barker-like sequences, prime lengths ≤ 47.
- Statistic: max normalized autocorrelation deviation across code/rotation.
- Null: 10,000 Gaussian phase randomizations with identical power spectrum.
- Decision: one-tailed p with Bonferroni correction for the code family size.
Appendix B — Bits in Constants (Feasibility)
Let x be a dimensionless constant with measured value x̂ and uncertainty σ. The per-constant channel capacity (bits) under Gaussian noise with tolerance τenc is approximately:
Aggregate across near-orthogonal constants; penalize for correlations and long-term drifts. If Σ Cx ≪ 1, constants are a poor carrier.
Appendix C — Black-Hole Yield Sensitivity Map
Define a minimal parameter vector θ = { α, me/mp, Q, G }, then:
Publish contour plots of YBH(θ). Ridges support selection-style reproduction stories; flatlands don't.
Appendix D — Mathematical Definitions & Identities
- Spherical harmonics: coefficients aℓm with Cℓ = 1/(2ℓ+1) Σm |aℓm|²
- Matched circles (topology): statistic S maximizing phase correlations along paired great-circle arcs.
- Compression/MDL: ΔDL = DL(model) − DL(null); positive ΔDL favors the model if penalties are included.
- Algorithmic proxies: Lempel–Ziv complexity KLZ as an upper-bound proxy for Kolmogorov complexity.
- Persistent homology: multiscale homology groups with barcodes; summary by Betti numbers βk(τ) and Euler characteristic χ.
- Reed–Solomon: code over GF(q) with parameters (n,k) correcting up to ⌊(n−k)/2⌋ symbol errors; useful for short robust payloads.